Need full solution and add jot notes next to steps if needed so that I can better understand the solution. Consider the heat equationдиƏt=J²uმ2subject to the boundary conditions+u, 00,u(0,t) = u(L,t) = 0.Suppose2πx5πxu(x, 0) = 3 sin-- 8 sinLLwhere is a positive constant.a) Use separation of variables to solve the problem.b) Evaluatelim u(x,t).0047Does the value of the constant play a role in this limit? Explain.

Answered: Image /qna-images/answer/fa4add65-4544-4eaa-a96f-fd2cf530e5e0.jpg

Answered: Consider the heat equation ди Ət = J²u…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The equations ry? + 8zzcos(u) + ye" = 16 and r*yz + xe" – 5u²v² = 15 are solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v) = (5,0). Find (),y at P. %3D
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The equations xy² + 8xzcos(u) + ye" : = 16 and x'yz + xe" – 5u?v² = 15 are solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v) = (5,0). Find ( ).,y at P. az Türkçe: xy? + 8xzcos(u) + ye" = 16 ve x³yz + xe® – 5u?v² = 15 denklemleri P noktası (x,y,z)=(1,1,1) ve (u, v) = (5,0) civarında x,y ve z'nin fonksiyonu olmak üzere u ve v için Çözümlü olsun. P'de (u), a )z,y yi hesaplayınız.) 16,00 O -50,00 O 40,00 O -0,12 O -40,00
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